Question

abcd is parrelelogram am and bn are respectively the perpendicular from a and b to dc and cd produced . prove that am bn

Answer 1

Answer:

Step-by-step explanation:

Simply,ABCD is a parralelogram hence AB II CD

AM and BN are perpendiculars{distances b/w AB and CD}

Distances b/w II lines is constant hence

AM=BN

Answer 2

Given:

ABCD is a parallelogram.

AM and BN are perpendicular to DC and CD respectively.

To Find:

AM = BN

Solution:

In ΔADM and ΔBCN,

opposite sides of a parallelogram are equal so,

AD = BC

Now, both angles M and N are 90°

∴ ∠AMD = ∠BND = 90°

We know that corresponding angles are equal and AD is parallel to BC and Dc is transversal.

∴ ∠ADM = ∠BCN

Then, ΔADM ≅ ΔBCN  [By the AAS congruency rule]

AM = AN [By C.P.C.T]

Hence proved that AM is equal to AN.